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Analytical Mechanics,9780534494926
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Analytical Mechanics

by ;
Edition:
7th
ISBN13:

9780534494926

ISBN10:
0534494927
Format:
Hardcover
Pub. Date:
3/19/2004
Publisher(s):
Cengage Learning
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Summary

Master introductory mechanics with ANALYTICAL MECHANICS! Direct and practical, this physics text is designed to help you grasp the challenging concepts of physics. Specific cases are included to help you master theoretical material. Numerous worked examples found throughout increase your problem-solving skills and prepare you to succeed on tests.

Table of Contents

1 Fundamental Concepts: Vectors
1(46)
1.1 Introduction
1(1)
1.2 Measure of Space and Time: Units and Dimensions
2(7)
1.3 Vectors
9(6)
1.4 The Scalar Product
15(4)
1.5 The Vector Product
19(3)
1.6 An Example of the Cross Product: Moment of a Force
22(1)
1.7 Triple Products
23(2)
1.8 Change of Coordinate System: The Transformation Matrix
25(5)
1.9 Derivative of a Vector
30(1)
1.10 Position Vector of a Particle: Velocity and Acceleration in Rectangular Coordinates
31(5)
1.11 Velocity and Acceleration in Plane Polar Coordinates
36(3)
1.12 Velocity and Acceleration in Cylindrical and Spherical Coordinates
39(8)
2 Newtonian Mechanics: Rectilinear Motion of a Particle
47(35)
2.1 Newton's Law of Motion: Historical Introduction
47(13)
2.2 Rectilinear Motion: Uniform Acceleration Under a Constant Force
60(3)
2.3 Forces that Depend on Position: The Concepts of Kinetic and Potential Energy
63(6)
2.4 Velocity-Dependent Forces: Fluid Resistance and Terminal Velocity
69(6)
2.5 Vertical Fall Through a Fluid: Numerical Solution
75(7)
3 Oscillations
82(62)
3.1 Introduction
82(2)
3.2 Linear Restoring Force: Harmonic Motion
84(9)
3.3 Energy Considerations in Harmonic Motion
93(3)
3.4 Damped Harmonic Motion
96(10)
3.5 Phase Space
106(7)
3.6 Forced Harmonic Motion: Resonance
113(12)
3.7 The Nonlinear Oscillator: Method of Successive Approximations
125(4)
3.8 The Nonlinear Oscillator: Chaotic Motion
129(6)
3.9 Nonsinusoidal Driving Force: Fourier Series
135(9)
4 General Motion of a Particle in Three Dimensions
144(40)
4.1 Introduction: General Principles
144(7)
4.2 The Potential Energy Function in Three-Dimensional Motion: The Del Operator
151(5)
4.3 Forces of the Separable Type: Projectile Motion
156(11)
4.4 The Harmonic Oscillator in Two and Three Dimensions
167(6)
4.5 Motion of Charged Particles in Electric and Magnetic Fields
173(3)
4.6 Constrained Motion of a Particle
176(8)
5 Noninertial Reference Systems
184(34)
5.1 Accelerated Coordinate Systems and Inertial Forces
184(5)
5.2 Rotating Coordinate Systems
189(7)
5.3 Dynamics of a Particle in a Rotating Coordinate System
196(5)
5.4 Effects of Earth's Rotation
201(6)
5.5 Motion of a Projectile in a Rotating Cylinder
207(5)
5.6 The Foucault Pendulum
212(6)
6 Gravitation and Central Forces
218(57)
6.1 Introduction
218(5)
6.2 Gravitational Force between a Unifirm Sphere and a Particle
223(2)
6.3 Kepler's Laws of Planetary Motion
225(1)
6.4 Kepler's Second Law: Equal Areas
226(3)
6.5 Kepler's First Law: The Law of Ellipses
229(9)
6.6 Kepler's Third Law: The Harmonic Law
238(6)
6.7 Potential Energy in a Gravitational Field: Gravitational Potential
244(6)
6.8 Potential Energy in a General Central Field
250(1)
6.9 Energy Equation of an Orbit in a Central Field
251(1)
6.10 Orbital Energies in an Inverse-Square Field
251(6)
6.11 Limits of the Radial Motion: Effective Potential
257(3)
6.12 Nearly Circular Orbits in Central Fields: Stability
260(2)
6.13 Apsides and Apsidal Angles for Nearly Circular Orbits
262(2)
6.14 Motion in an Inverse-Square Repulsive Field: Scattering of Alpha Particles
264(11)
7 Dynamics of Systems of Particles
275(48)
7.1 Introduction: Center of Mass and Linear Momentum of a System
275(3)
7.2 Angular Momentum and Kinetic Energy of a System
278(5)
7.3 Motion of Two Interacting Bodies: The Reduced Mass
283(5)
7.4 The Restricted Three-Body Problem
288(15)
7.5 Collisions
303(3)
7.6 Oblique Collisions and Scattering: Comparison of Laboratory and Center of Mass Coordinates
306(6)
7.7 Motion of a Body with Variable Mass: Rocket Motion
312(11)
8 Mechanics of Rigid Bodies: Planar Motion
323(38)
8.1 Center of Mass of a Rigid Body
323(5)
8.2 Rotation of a Rigid Body about a Fixed Axis: Moment of Inertia
328(2)
8.3 Calculation of the Moment of Inertia
330(8)
8.4 The Physical Pendulum
338(6)
8.5 The Angular Momentum of a Rigid Body in Laminar Motion
344(3)
8.6 Examples of the Laminar Motion of a Rigid Body
347(7)
8.7 Impulse and Collisions Involving Rigid Bodies
354(7)
9 Motion of Rigid Bodies in Three Dimensions
361(56)
9.1 Rotation of a Rigid Body about an Arbitrary Axis: Moments and Products of Inertia Angular Momentum and Kinetic Energy
361(10)
9.2 Principal Axes of a Rigid Body
371(10)
9.3 Euler's Equations of Motion of a Rigid Body
381(2)
9.4 Free Rotation of a Rigid Body: Geometric Description of the Motion
383(1)
9.5 Free Rotation of a Rigid Body with an Axis of Symmetry: Analytical Treatment
384(7)
9.6 Description of the Rotation of a Rigid Body Relative to a Fixed Coordinate System: The Eulerian Angles
391(6)
9.7 Motion of a Top
397(4)
9.8 The Energy Equation and Nutation
401(6)
9.9 The Gyrocompass
407(2)
9.10 Why Lance Doesn't Fall Over (Mostly)
409(8)
10 Lagrangian Mechanics 417(48)
10.1 Hamilton's Variational Principle: An Example
419(4)
10.2 Generalized Coordinates
423(3)
10.3 Calculating Kinetic and Potential Energies in Terms of Generalized Coordinates: An Example
426(4)
10.4 Lagrange's Equations of Motion for Conservative Systems
430(1)
10.5 Sone Applications of Lagrange's Equations
431(7)
10.6 Generalized Momenta: Ignorable Coordinates
438(6)
10.7 Forces of Constraint: Lagrange Multipliers
444(5)
10.8 D'Alembert's Principle: Generalized Forces
449(6)
10.9 The Hamiltonian Function: Hamilton's Equations
455(10)
11 Dynamics of Oscillating Systems 465
11.1 Potential Energy and Equilibrium: Stability
465(4)
11.2 Oscillation of a System with One Degree of Freedom about a Position of Stable Equilibrium
469(3)
11.3 Coupled Harmonic Oscillators: Normal Coordinates
472(21)
11.4 General Theory of Vibrating Systems
493(5)
11.5 Vibration of a Loaded String or Linear Array of Coupled Harmonic Oscillators
498(7)
11.6 Vibration of a Continuous System: The Wave Equation
505
Appendix A Units A-1
Appendix B Complex Numbers and Identities A-4
Appendix C Conic Sections A-7
Appendix D Service Expansions A-11
Appendix E Special Functions A-13
Appendix F Curvilinear Coordinates A-15
Appendix G Fourier Series A-17
Appendix H Matrices A-19
Appendix I Software Tools: Mathcad and Mathematica A-24
Answers to Selected Odd-Numbered Problems ANS-1
Selected References R-1
Index I-1


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